The present invention relates generally to sonar arrays, and, more particularly, to a method for doubling the resolving power of a sonar array, e.g., a side-scanning or sector-scanning, pulsed-transmission, echo ranging sonar system, and a sonar array which implements this method.
In general, a sonar array consists of an arrangement of appropriately spaced-apart sonar transducers or projectors which convert electrical energy generated by a sonar transmitter into sound waves which are launched by the projectors into surrounding water. The sound waves, which collectively constitute an acoustic beam, travel through an area of surrounding water subtended by the beam to detect and locate objects, such as mines and submarines, which may be present in this area of the water. These objects are known as sonar targets. By appropriately controlling the phase and amplitude of the electrical signals applied to the individual sonar projectors, using a beam forming and steering network, a plurality of beams having different shapes and profiles can be formed and steered, to thereby scan a desired coverage area. The area of the water and/or sea floor that is acoustically imaged in the course of a sonar scan is sometimes referred to as the "ensonification field". The sonar targets located in the ensonification field, reflect or scatter the beam, to thereby produce return or echo sound signals (or simply, "echo") which are converted into appropriate electrical signals by an array of appropriately spaced-apart transducers or hydrophones. The electrical signals produced by the hydrophones are then fed to a sonar receiver. These electrical signals, which are representative of the echo, are then processed by receiver electronics and displayed in intelligible form for use by sonar personnel in identifying and/or locating the sonar target(s). Of course, the transmitter and receiver can be embodied as an integrated transmitter/receiver (transceiver) which can be switched between transmit and receive modes of operation.
To facilitate a better understanding of the ensuing description of the present invention, certain fundamentals of array theory will now be briefly reviewed. More particularly, with reference now to FIG. 1, there can be seen a linear or line array 20 which includes a plurality, N.sub.e, of hydrophone elements 22 whose acoustic centers are periodically spaced at intervals d along the x-axis. This line array 20 can be used to steer a plurality of beams relative to the array broadside. The general point-reflector response function for any line array, subject only to the restriction that the field point is sufficiently far from the array that the spherical amplitude spreading term is negligibly different across the array, can be written as: ##EQU1## where R.sub.o is the distance from the first array element to the field point, .theta. is the relative bearing angle to the field point, W.sub.i are the complex beam forming coefficients applied to the hydrophone array (e.g., to effect amplitude shading, beam steering, beam focusing, and calibration), .omega. is the frequency of the beam, in radians, t is time, k is 2.pi./.lambda.(where .lambda. is the wavelength of the beam), Rt is the distance from the projector 24 to the field point, and Rri are the distances from the field point to the i.sup.th array element at the time of echo reception. If the distance from the field point to the array is large compared to both the wavelength and the array length, then the distance traveled by the wave front from the field point to the i.sup.th element differs from the distance to the first element by: EQU .delta.=d(i-1)sin .theta.. (2)
In that case, Equation (1) can be written as: ##EQU2## Several terms can be moved outside of the summation and ignored since they contribute only a constant phase shift, to thereby yield the following equation: ##EQU3## An expression for the resolution of an unshaded, unfocused, unsteered array can be derived by selecting W.sub.i =1/N.sub.e, and neglecting the time dependence, whereby equation (4) can be further simplified to: ##EQU4## This finite series is recognized as a geometrical progression, the sum of which is contained in the bracketed term below: EQU P(.theta.)=1/N.sub.e [(e.sup.-jkdNesin.theta. -1)/(e.sup.-jkdsin.theta. -1)](6)
Using Euler's formulae, the magnitude of the pressure field can be expressed as: EQU P(.theta.)=sin((N.sub.e .pi.d/.lambda.)sin.theta.)/N.sub.e sin((.pi.d/.lambda.)sin .theta.), (7)
which is referred to as the "array factor". The radiation pattern of an individual array element of length D (i.e., the "element directivity pattern") is: EQU P.sub.E (.theta.)=sin((.pi.D/.lambda.)sin.theta.)/((.pi.D/.lambda.)sin.theta.) (8)
In accordance with the well-known "product theorem", the net array directivity pattern is the product of the array factor and the element directivity pattern. In the special case of a filled array, in which d=D, the result is the following well-known sine (x) pattern of an unshaded line array: EQU P.sub.E (.theta.)=sin((N.sub.e .pi.d/.lambda.)sin.theta.)/((.pi.d/.lambda.)sin.theta.). (9)
Inspection of equation (10) reveals that the first null in the pattern occurs at an angle given by: EQU .theta..sub.pn =sin.sup.-1 (.lambda./N.sub.e d), (10)
where .theta..sub.pn is the peak-to-null beam width. Further, the half-power beam width, which is usually considered to constitute the resolution limit in the Rayleigh sense, is given by: EQU .theta..sub.-3dB =0.88.theta..sub.pn =0.88sin.sup.-1 (.lambda./L), (11)
where L is the total array length, which equals N.sub.e d. Otherwise stated, equation (11) represents the fundamental, diffraction-limited, azimuthal resolution limit (i.e., maximum resolving power) of a conventional sonar array.
For a more detailed treatment of the above and other aspects of array and electroacoustics theory, reference may be made to the textbook Antenna Theory (Part 1), R. E. Collins, (McGraw-Hill, New York, 1969), pp. 146-147, the textbook Antenna Theory and Practice, R. Chatterjee, (John Wiley & Sons, New York, 1988), pp. 86-87, and the textbook Theory of Electroacoustics, J. Merhaut, (McGraw-Hill, New York, 1981), pp. 172-173.
Because the physical length of the array (i.e., the available aperture space) is almost always limited by system considerations, many efforts have been made in the past to develop techniques for maximizing the resolving power of the array within those physical constraints. In this connection, several techniques have been heretofore developed in order to enhance the effective resolution of conventional sonar arrays having a given physical array length, including monopulse transmission, maximum entropy, and maximum likelihood signal processing. However, the effectiveness of all of these "super-resolution" techniques is dependent upon and limited by (i.e., is a function of) the signal-to-noise (S/N) ratio of the system.
Based on the above, it can be appreciated that there presently exists a need in the art for a method for improving the resolution of a sonar array which can be used in lieu of or in addition to presently available resolution enhancement techniques, and whose effectiveness is not a function of the S/N ratio of the system. The present invention fulfills this need.